Mean Definition and 1000 Threads

Consider an oblique circular cone of altitude h, base radius R, with apex directly above a point on the base circumference. What is the mean length (& variance) for the set of all rays from the apex to points on or within the base circumference?

What does it mean to be "good at math"? I have recently began preparing for college by picking up a calculus textbook and doing it from the beginning. Although I'm not particularly talented at math, I am a little above average when it comes to understanding physics and mathematics concepts. I...

I was reading the Wikipedia article at http://en.wikipedia.org/wiki/Euler-Lagrange_equation and came across several symbols I am not familiar with. An arrow pointing right with a short vertical bar on the left end. What does this special arrow mean? How is it different from an arrow without the...

I understand the "north" is where to field is "coming out of" and south is where it returns, and i can see how two magnets would repel and attract. However when electrons or protons are brought near magnetic fields they are deflected. Why? What determines which direction a negativley charged...

Using second mean value theorem in Bonnet's form show that there exists a $$p $$in $$[a,b]$$ such that $$\int_a^b e^{-x}cos x dx =sin ~p$$ I know the theorem but how to show this using that theorem .

If I have a problem in which the laminar/turbulent transition point is said to be 50% the mean aerodynamic chord, how can I find the area of the wing over which there is laminar flow? Is it simply half the wing area?

I could see that capacitor impedance is mostly negative. Does the negative sign has any significant meaning? Also why do people convert impedance to admittance for circuit calculation? Please help!

Homework Statement Calculate the mean square displacement x2 of the particle from its equilibrium position.Homework Equations ∫ from -\infty to +\infty of Nv2 * Hv(y) * e-y^2 dy Since y=x/\alpha, \alphady=dx yHv = vHv-1 + (1/2)Hv+1The Attempt at a Solution...

Hey! I've been doing some research on random walks. From what I have gathered, a random walker in 1-D will have: <x> = [FONT="Georgia"]N l (2 p - 1) σ =[FONT="Georgia"] 2 l sqrt[N p (1 - p) ] Here, N is the number of steps, p is the probability to take a step to the right and l is the step...

Homework Statement What is the expected value of ||Ax+n|| where || || is the L2 norm and x and n are uncorrelated and E[n] = 0 The Attempt at a Solution E[ norm of Y] = E[(Ax+n)' (Ax+n)] = E[(x'A'+n')(Ax+n)] = E[x'A'xA +x'T'n +n'Ax +n'n] the three last terms = 0 due to...

Homework Statement Random vector Y = [Y_1 Y_2 Y_3 …. Y_m]' where ' = transpose mean = u and and ∑ = covariance Z = N_1 * Y_1 + N_2 * Y_2 + …. + N_m*Y_m all N are numbers Find the covariance of Z E[ (Y- E[Y] )(Y - E[Y] ) ] = E[YY'] -E[Y]E[Y]'= [N_1 N_2 .. N_m] [∑ - u^2 ….∑ -u^2] ' This...

Find the mean square error using the pseudo inverse approach. I am given a 11X9 matrix A, a 11X1 vector F and R = 11X11 diagonal matrix so Rhat = A[(A'A)^-1 ]A' R . Then I get a 11X11 matrix. Shouldn't I get getting a 8X11 matrix How do I get the most optimum vector F?

"you know for a fact that a bowling ball drops more quickly than a feather. This is true, but it has nothing to do with gravity. The only reason this occurs is because the earth’s atmosphere provides resistance. " friction??

I have a doubt about the interference wave pattern of double slit experiment with light beam. does it mean the interference of electromagnetic wave (which tells about the frequency causing color) or Spatial probability wave (which was explained by Max Born). I am not good at math. can someone...

Homework Statement "At 273 K and 1.00x10^-2 atm, the density of a gas is 1.24x10^-5 g/cm^3. A.) Find the Vrms for the gas molecules B.) Find the molar mass and identify the gas (Choose from H2, He, H20, N2, O2, or CO2)" Homework Equations Vrms = √(3RT/Mm) pV = nRT The Attempt...

"consider the collection of all polynomials (with complex coefficients) of degree less than N in x" okay so I'm considering a set of polynomials with complex coefficients and degree of the polynomial is less than N. what is this "in x" part that's being referred to? what's x?...

[a;b[ I want to do a problem with this but i can't find anything about it, if anyone can help me it'd be very useful, thank you. :) The one i want to do exactly is [20;30[ , in case anyone is wondering.

The link to the motor is here: http://www.savoxusa.com/Savox_SC1256TG_Digital_Servo_p/savsc1256tg.htm In the description tab, it lists all the specs. My question is in regards to the speed specs. e.g., "Speed(@4.8V sec/60): .18" I don't understand what that is saying. 0.18 what? 0.18 sec per...

f = 1/T?? What does it mean? What does this formula means: f = 1/T I don't get this. Please explain the relationship between frequency and period and the formula above thanks :)

Homework Statement A tyre contains gas at a pressure of 150 kPa. If the gas has a density of 2.0 kg m-3, find the root mean square speed of the molecules. Homework Equations These are the equations I believe to be relevant: c_{rms} = \frac{\sqrt{<c^2>}}{N} pV = \frac{1}{3}Nm<c^2> p =...

How to calculate <n_i ^2> for an ideal gas by the grand partition function (<n_i> is the occupation number)? In other words, I like to know how do we get to the formula <n_i>=-1/\beta (\frac{\partial q}{\partial\epsilon}) and <n_i ^2>=1/Z_G [-(1/\beta \frac{\partial }{\partial\epsilon})^2 Z_G]...

I have been debating with a few other people on another board, regarding the correct way to calculate the mean average of a list of values, where those values are recorded temperatures. A great many people seem to believe, for example, that if each temperature reading is accurate to +/- 0.5°...

I found this equation for driven oscillators, and am unsure what the F_0 means, and how it's used. Can someone please briefly explain this? Also, I don't get what the difference is between the initial and final omega. (how can there be a final omega if it's constantly increasing?)

Homework Statement Homework Equations The Attempt at a Solution I am confused as to which streams I should use for the log mean temperature difference. I am pretty sure it should be the difference in temperature between the two streams on the same side, so I think it's (700-450)-(1100-960) /...

I hear this term a lot but couldn't find much from a google search My initial guess is that we put a AC current through a inductor coil to create a magnetic field. Am I close?

With mean = 2 with exponential distribution Calculate E(200 + 5Y^2 + 4Y^3) = 432 E(200) = 200 E(5Y^2) = 5E(Y^2) = 5(8) = 40 E(4Y^3) = 4E(Y^3) = 4(48) = 192 E(Y^2) = V(Y) + [E(Y)]^2 = 2^2+2^2= 8 E(Y^3) = m_Y^3(0) = 48(1-2(0))^{-4} = 48 is this right?

Physics teacher and physics professors need to come up with a better definition of nonlinearity if we expect our students to pass any basic physics course. This is because of how education has changed over the past 10 years. I hope in this thread, we collectively as members of this forum can...

So I have been doing research and if antimatter atoms can exist, does that mean every atom now a days has an antimatter counterpart? I know we have discovered anti-hydrogen but anyways I'm trailing off. Could you theoretically create anti-molecules? Obviously realistically at this time...

I was given a C++ program (a hefty one at that) and asked to create a map of it. He added some more details (something about functions), and I left his office thinking I understood what he requested but now I realize I don't. I'll approach him and ask for more details but before I do that...

My book has a chapter on the general mean field approach. I have attached a page of it I don't understand very well. I do understand the general idea of meanfield theory: Expand operators around their average and assume small fluctuations and neglect the second order term. But in the attached...

Homework Statement For the nonparameteric estimator \hat{f}(x)=\frac{1}{2hn}\sum\limits_{i=1}^n I_i(x) of a pdf, (a) Obtain its mean and determine the bias of the estimator (b) Obtain its variance Homework Equations The Attempt at a Solution For (a), I think it goes like this...

We have variable X (Active companies with a credit score) and variable Y (Bankrupt companies with a credit score) The mean, variance, n etc for their credit scores are known for X and Y. (We are given a lot of information about these companies, but a lot of this information is irrelevant...

What does the definition" the energy is not continuous" mean? Title is the whole question

Homework Statement An ideal gas has rms speed vrms at a temperature of 288K . At what temperature is the rms speed tripled? Homework Equations P=(NmV2)/3V The Attempt at a Solution I'm kind of stumped on this one. Other ones I've done are pretty simple to figure out, but the...

Hi guys, I hope someone is able to help me with this, I'm currently stuck on a problem. 1. I was given some data (in continuous, grouped form) regarding phone call times for a call center agent and asked to represent the data using the most accurate form of average. I initially calculated...

Hi guys, I hope someone is able to help, I'm currently stuck on a problem. I'm having trouble justifying which representation is more accurate for my data; either mean with standard deviation or median with IQR. I've calculated both averages for the my data, however I was advised by someone...

If I have a collection of vectors in very high euclidean space(n=72). How do I find the mean value of all the vectors? Maybe I'm using the incorrect terminology. Maybe I want to find the centroid of where all these vectors are?? I'm working on a machine learning algorithm. Any help would be...

Homework Statement Show in the graph ,there will be no allowed bound states with odd-parity if the well depth is less than ${V_min}$ Find ${V_min}$ in terms of k and a.where a is the half of the well width. What does no allowed bound state mean? Homework Equations $cotz=-pa/z$ where p^2...

Why is the geometric mean used to define the center frequency of a bandpass filter instead of the arithmetic mean? I read in this book that 1. All the lowpass elements yield LC pairs that resonate at ω = 1. 2. Any point of the lowpass response is transformed into a pair of points of the...

I have been asking around campus to find software for checking 'gigantic' primes and this term popped up in my inbox today "chunked down number' So what in software language is a 'chunked down number'? They were concerned if using Java that this might be a problem for prime verification of...

Homework Statement Suppose that: E(X1) = μ, Var(X1) = 7, E(X2) = μ, Var(X2) = 13, E(X3) = μ, and Var(X3) = 20, and consider the point estimates: μˆ1 = X1/3 + X2/3 + X3/3 μˆ2 = X1/4 + X2/3 + X3/5 μˆ3 = X1/6 + X2/3 + X3/4 + 2 (a) Calculate the bias of each point estimate. Is...

Suppose I have two atoms that independently emit alpha particles. I want to find the mean \Delta T for the events. I then want to extend this for 3, 4 etc. atoms however what I'd like to do for more than 3 atoms is find the smallest delta T for any two emissions. What should I look at to...

Why does a higher activation energy usually mean a slower reaction? Doesn't activation energy just tell us whether or not a reaction will take place or not based on if the particles have enough energy to meet the activation barrier? How is it related to the rate of the reaction?

What does "a function takes on" mean? Hey! I'm currently learning Picard's theorem, but I don't quite understand it because of difficult words.. In the text, it uses the term "takes on", ie "If f(z) is analytic and has an isolated essential singularity at a point z_0, it takes on every...

Homework Statement Let u be a harmonic function in the open disk K centered at the origin with radius a. and ∫_K[u(x,y)]^2 dxdy = M < ∞. Prove that |u(x,y)| \le \frac{1}{a-\sqrt{x^2+y^2}}\left( \frac{M}{\pi}\right)^{1/2} for all (x,y) in K. Homework Equations Mean value property for...

Homework Statement There are a set number of marbles in a bag; the marbles consist of two colors. We are given the mean number of marbles of color 1 in the bag, as well as color 1's standard deviation. We are then asked to find the mean and standard deviation of color 2.Homework Equations How...

Homework Statement http://i.minus.com/jX32eXvLm6FGu.png Homework Equations The MVT applies if 1) The function is continuous on the closed interval [a,b] such that a<b. 2) The function is differentiable on the open interval (a,b) And if the above two conditions are fulfilled...

So I took a series of measurements, where the reading error for the measurements are either ±0.01 mm or ±0.02 mm or ±0.03 mm or ±0.04 mm. Now, I can calculate the estimated mean of the measurements by x_est=Ʃ x_i / N, where x_i is the i th measurement. Then I can propagate the errors in the...

Hi there , I have some simple (on 1st look) questions. I just need some help.http://img59.imageshack.us/img59/3018/5hby.png 1st question. I think the expected value should be 150 since the probability of getting a head is 1/2 .. 300x1/2 = 150 so the mean should also be 150. the variance...

if b is the mean proportion between a and c ,show that abc(a+b+c)^3 = (ab+bc+ca)^3